In this paper, we consider the exact boundary controllability for cubic focusing semilinear wave equations in $1\le n\le 3$ space dimensions. When the initial data and the final data are in the so-called potential well, we find that the sufficient condition for the global existence is also sufficient to ensure the exact boundary controllability of the problem. Moreover, in one space dimension, the control time can be that of the linear wave equation.
"Potential well and exact boundary controllability for semilinear wave equations." Adv. Differential Equations 16 (11/12) 1021 - 1047, November/December 2011.